Related papers: A gauge theory for the 2+1 dimensional incompressi…
We study a model of massive photons with a parity invariant and non-local mass term. We identify a discrete symmetry of the classical equations of motion and show that this symmetry can be thought of as an electric-magnetic duality valid…
$p$-form electrodynamics in $d\geq 2$ dimensions is shown to emerge as the edge modes of a topological field theory with a precise set of boundary conditions, through the Hamiltonian reduction of its action. Electric and magnetic charges…
In this article we review some of the recent advances regarding the charged vortex solutions in abelian and nonabelian gauge theories with Chern-Simons (CS) term in two space dimensions. Since these nontrivial results are essentially…
We study a $U(1) \times U(1)$ gauge theory discussing its vortex solutions and supersymmetric extension. In our set-upon the dynamics of one of two Abelian gauge fields is governed by a Maxwell term, the other by a Chern-Simons term. The…
We consider a system of nonlinear equations that extends the Maxwell theory. It was pointed out in a previous paper that symmetric solutions of these equations display properties characteristic of magnetic oscillations. In this paper I…
The procedure of null reduction provides a concrete way of constructing field theories with Galilean invariance. We use this to examine Galilean gauge theories, viz. Galilean electrodynamics and Yang-Mills theories in spacetime dimensions 3…
We review nonlinear gauge theory and its application to two-dimensional gravity. We construct a gauge theory based on nonlinear Lie algebras, which is an extension of the usual gauge theory based on Lie algebras. It is a new approach to…
The asymptotic properties of conformally static metrics in Einstein-aether theory with a perfect fluid source and a scalar field are analyzed. In case of perfect fluid, some relativistic solutions are recovered such as: Minkowski spacetime,…
It has previously been proposed that the the theory of strings and branes possesses a large symmetry group generated by the Kac-Moody algebra $E_{11}$. It has also previously been proposed that the the theory of gravitation in four…
We present two-dimensional gauged Lifshitz scalar field theories by considering the duality relation between the source current and the Noether current. Requiring the duality partially, we obtain a gauged model which recovers the bosonized…
The concept of a fluid algebra was introduced by Sullivan over a decade ago as an algebraic construct which contains everything necessary in order to write down a form of the Euler equation, as an ODE whose solutions have invariant…
We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely…
This study develops an effective theoretical framework that couples two vector fields: the velocity field $\mathbf{u}$ and an auxiliary vorticity field $\boldsymbol{\xi}$. Together, these fields form a larger conserved dynamical system.…
We show that a certain class of vortex blob approximations for ideal hydrodynamics in two dimensions can be rigorously understood as solutions to the equations of second-grade non-Newtonian fluids with zero viscosity, and initial data in…
Using a generalised Noether prescription we are able to extract all the currents and their conservation laws in space dependent shift symmetric theories. Various identities among the currents in the matter sector are found that form the…
One field of fluid dynamics concerns the search for variational principles. So far, the Hamiltonian view and Riemannian geometry has been applied to find geodesics for hydrodynamic systems. Compared to Riemannian geometry sub-Riemannian…
We use Noether symmetry approach to find spherically symmetric static solutions of the non-minimally coupled electromagnetic fields to gravity. We construct the point-like Lagrangian under the spherical symmetry assumption. Then we…
The purpose of this work is to prove existence of a weak solution of the two dimensional incompressible Euler equations on a noncylindrical domain consisting of a smooth, bounded, connected and simply connected domain undergoing a…
In this paper we consider external current QED in the Coulomb gauge and in axial gauges for various spatial directions of the axis. For a non-zero electric charge of the current, we demonstrate that any two different gauges from this class…
A two-dimensional nonlinear gauge theory that can be proposed for generalization to higher dimensions is derived by means of cohomological arguments.